Finite Group DatabasebetaFinite Group Databasebeta| order | 33536 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C131 · Schur multiplier (H2) = C26 |
| direct product | C131×#33361 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C131 | C22×#99 |
| commutator | C2×C4 | C23×C4×C131 |
| Frattini, cosocle | C2×D4 | C24×C131 |
| prime radical | #3500×C131 | C2 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C131 ◁ C2×D4×C131 ◁ C2×H(5,𝔽2)×C131 ◁ G | |
1252 conjugacy classes of subgroups.
| minimal degree | μ(G) = 163 |
| transitive degree | μt(G) = 4192 |
A minimal faithful permutation representation — 4 generators on 163 points:
(1,2)(3,11,14,24)(4,8)(5,17,19,9)(6,10)(7,13)(12,25,26,32)(15,22)(16,29,28,23)(18,21)(20,27)(30,31)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163);(1,3,6,14)(2,7,10,21)(4,12,15,26)(5,18,19,13)(8,20,22,31)(9,24,17,11)(16,30,28,27)(23,32,29,25);(1,4)(2,8)(3,12)(5,16)(6,15)(7,20)(9,23)(10,22)(11,25)(13,27)(14,26)(17,29)(18,30)(19,28)(21,31)(24,32);(4,15)(8,22)(12,26)(16,28)(20,31)(23,29)(25,32)(27,30)6026 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33536, 26349);